gquantile

Quantiles of a grouped sample.

In some scientific works, once the data have been gathered from a population of interest, it is often difficult to get a sense of what the data indicate when they are presented in an unorganized fashion.

Assembling the raw data into a meaningful form, such as a frequency distribution, makes the data easier to understand and interpret. It is in the context of frequency distributions that the importance of conveying in a succinct way numerical information contained in the data is encountered.

So, grouped data is data that has been organized into groups known as classes. The raw dataset can be organized by constructing a table showing the frequency distribution of the variable (whose values are given in the raw dataset). Such a frequency table is often referred to as grouped data.

Here, we developed a m-code to calculate the quantile(s) of a grouped data. One can input the returns or modified vectors n and xout containing the frequency counts and the bin locations of the hist m-function, in a column form matrix.

Quantile calculation uses the straight forward formula,

R = L + I*(N*Q - C)/F

where:
L = lower limit of the interval containing the quantile
I = width of the interval containing the quantile
N = total number of data
Q = interested quantile
C = cumulative frequency corresponding to the previous quantile class
F = number of cases in the interval containing the quantile

In orden to run it you must first download the m-file gprctile at:
http://www.mathworks.com/matlabcentral/fileexchange/38228-gprctile

Syntax: function y = gquantile(x,p)

Inputs:
x - data matrix (Size of matrix must be n-by-2; absolut frequency=column 1, class mark=column 2)
p - scalar or a vector of cumulative probability values

Outputs:
y - quantile(s) of the values in x